A quantum mechanical mind-body interaction

The reduction of a quantum mechanical wave function by the entry of a datum into the consciousness of an observer is used, in a semirealistic neurochemical model, to bring about excitation of a nerve cell in that observer's central nervous system. It is suggested that mind can induce muscular movements by choosing to note data originating from specialized elements of the nervous system. Only the freedom to note or not to note a relevant datum is postulated for the observer's mind; the consequences of either choice are deterministic on the neural scale of events, so that quantum indeterminacy is consistent with physiological determinacy. The proposed mind-body coupling depends on the possibility of the biological evolution of a macroscopic device which has strikingly different neural correlates of its pure and mixed quantum states, respectively. An example of such a device is outlined in terms of components which are familiar from existing nervous systems.     

Automorphisms of groups and of schemes of finite type

We show first that certain automorphism groups of algebraic varieties, and even schemes, are residually finite and virtually torsion free. (A group virtually has a property if some subgroup of finite index has it.) The rest of the paper is devoted to a study of the groups of automorphisms. Aut(Γ) and outer automorphisms Out(Γ) of a finitely generated group Γ, by using the finite-dimensional representations of Γ. This is an old idea (cf. the discussion of Magnus in [11]). In particular the classes of semi-simplen-dimensional representations of Γ are parametrized by an algebraic varietyS _n (Γ) on which Out(Γ) acts. We can apply the above results to this action and sometimes conclude that Out(Γ) is residually finite and virtually torsion free. This is true, for example, when Γ is a free group, or a surface group. In the latter case Out(Γ) is a “mapping class group.” Partially supported by the NSF under Grant MCS 80-05802.     

Surface scattering in media with time and spatial dispersion

Scattering of scalar and vector waves from a randomly rough interface between media, in which several types of waves (modes) exist due to the time and spatial dispersion, has been studied in the Kirchhoff approximation. As a wave of a certain type is reflected from the interface, it transforms into other modes not only in the diffusive fields but in the coherent components as well. We have calculated the mean (coherent) field and the angular diagram of the diffusively scattered intensity. It is shown that the coherent components of the waves generated on reflection (cross-modes) propagate in directions that are different from the specular one. The dispersion gives rise to the frequency dependence of the scattering diagram even in the geometric-optics approximation.     

Rabi waves and Rabi wavepackets in one-dimensional quantum dot chain: Excitation,propagation, reflection

We theoretically investigate the spatial propagation of Rabi oscillations (Rabi waves) in one-dimensional inhomogeneous quantum dot (QD) chain. QD-chain is modeled by the set of two-level quantum systems with tunnel coupling between neighboring QDs. The space propagation of Rabi waves in the form of traveling waves and localized wave packets is considered. It is shown, that the propagation of Rabi waves is accompanied by the transfer of the inversion and quantum correlations along the QD-chain and by their reflection and mutual transformations at the spatial inhomogeneities of QE-chain. The effect is potentially applicable in quantum nanooptics and quantum informatics.     

Transverse velocity dependence of the proton-antiproton ratio as a signature of the QCD critical point

The presence of a critical point in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the mu_B-T phase diagram. If the average emission time of hadrons is a function of transverse velocity, as microscopic simulations of the hadronic freeze-out dynamics suggest, the deformation of the hydrodynamic trajectories will change the transverse velocity (beta_T) dependence of the proton-antiproton ratio when the fireball passes in the vicinity of the critical point. An unusual beta_T dependence of the [over]p/p ratio in a narrow beam energy window would thus signal the presence of the critical point.     

Working gases in thermoacoustic engines.

The best working gases for thermoacoustic refrigeration have high ratios of specific heats and low Prandtl numbers. These properties can be optimized by the use of a mixture of light and heavy noble gases. In this paper it is shown that light noble gas-heavy polyatomic gas mixtures can result in useful working gases. In addition, it is demonstrated that the onset temperature of a heat driven prime mover can be minimized with a gas with large Prandtl number and small ratio of specific heats. The gas properties must be optimized for the particular application of thermoacoustics; it cannot be assumed that high specific heat ratio and low Prandtl number are always desirable.     

Vibrational and 29Si NMR spectroscopies of soluble silicate oligomers

Vibrational spectroscopy has been used to correlate the features of silicate solution spectra with ²⁹Si NMR spectra, as a function of SiO₂:Na₂O ratio and SiO₂ concentration. Assignments of infrared and Raman component bands have been made for different anion types and are consistent with results reported for crystalline silicates and silicate glasses. The extent of depolymerization of larger anions has been found to differ, depending on both the degree of dilution and alkalinity. The relative amounts of polymeric (Q⁴) silica and larger three dimensional (Q³_4R) anions are greater for the more siliceous solutions (3.3 and 2.95 ratio) at high concentrations. These large anions continue to be major contributors to the anion distribution even at 15 to 50 fold dilution. In the case of more alkaline solutions, especially below 2.5 ratio, the relative contribution of the large anions to the distribution drops rapidly, even with 2 or 3 fold dilution. At low concentrations, in very alkaline solutions, the anion distribution is mainly monomer, dimer and cyclic trimer. Vibrational spectroscopies show great promise for observing changes in anion distribution on a much shorter time scale than is possible with ²⁹Si NMR and can be useful for following reactions involving silicate solutions.